How do you differentiate $-x^(2+1)$ ?

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Answer 1 · 2017-07-02T02:39:04

$d/(dx) -x^(2+1) = color(blue)(-3x^2$

We're asked to find the derivative of the expression

$-x^(2+1)$

This can be written as

$d/(dx) (-x^3)$

We can first factor out the constant, $-1$ :

$-1(d/(dx) x^3)$

Using the power rule:

$d/(dx) x^n = nx^(n-1)$

$d/(dx) x^3 = 3x^(3-1) = 3x^2$

Lastly, multiplying by $-1$ gives

$d/(dx) -x^3 = color(blue)(-3x^2$

How do you differentiate -x^(2+1)-x^(2+1)?